Template matching of occluded object under low PSNR

Digital Signal Processing 23 (2013) 870–878

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Digital Signal Processing www.elsevier.com/locate/dsp

Template matching of occluded object under low PSNR Jae-Chern Yoo, Chang Wook Ahn ∗ College of Information and Communication Engineering, Sungkyunkwan University, Suwon, Gyeonggi-Do, 440-746, Republic of Korea

a r t i c l e

i n f o

Article history: Available online 2 January 2013 Keywords: Identification Normalized cross correlation Occlusion Template matching

a b s t r a c t A robust template matching using occlusion-free correlation (OFC) coefficient is presented in this paper for the purpose of locating objects partially occluded under low PSNR (Peak Signal to Noise Ratio) environment. The OFC coefficient can effectively eliminate the negative effect of occlusion on matching score, resulting in providing better accuracy in recognizing and locating objects under bad environment. This algorithm provides a closed-loop scheme through a reliability assessment of occlusion detection which is able to check if the occlusion detection is well made. Extensive experimental results through occluded images with various noise levels demonstrate that the proposed algorithm is robust against objects partially occluded under low PSNR and superior in terms of the false alarm and miss rates in the identification problem. © 2012 Elsevier Inc. All rights reserved.

1. Introduction Template matching has been a classical approach to the problems of locating and recognizing of an object in an image. It has a wide range of applications including industrial inspection, image registration, target classification, and other computer vision applications. Template matching is to find the best match of a target, called template, from a given image with maximum correlation. It involves computing the similarities between the template and windows of the same size as the target, and then identifying the window that produces the highest matching score. However, the template matching of an occluded image remains still an unsolved problem where it presents only successful results for imaging conditions under relatively high PSNR (Peak Signal to Noise Ratio). There have been many attempts to improve these bounds, and they can be basically classified into three categories: featurebased [1–7], learning-based [8–14] and intensity-based [15–22]. The feature-based matching method first finds correspondence between salient features such as points, lines, chamfer and contours in the images. The matching process is then conducted with these features. Feature-based approaches have the great advantage of being able to deal with complicated imaging variations including rotation and illumination. However, these approaches may suffer from occlusion under low PSNR since their performance highly depends on the feature extraction whose accuracy is critically affected by the occlusion and noise conditions. In order to solve these problems, there have been various studies on learning-based approaches such as SVM (Support Vector Machine) [8,9], nonnegative matrix factorization (NMF) [10,11] and neural network

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classifier [12–14]. These algorithms work normally well when a little part of the object is occluded because of the training set free of occlusion. Practically, their performance is highly dependent on how close the training set is to actual occluding status otherwise they will have difficulties in identifying images occluded differently from training set. Intensity-based methods are primarily based on the comparison of intensity patterns in images via sum of absolute difference (SAD) [15,16] metrics. It involves moving the small reference template within the large scene image on a pixel-by-pixel basis followed by calculating the SAD to determine their similarity. The SAD can easily achieve image matching without feature extraction. However, changes in illumination during image acquisition cause direct variations in intensity value, thus leading to failure in detecting the target. Many image matching methods have used Normalized Cross Correlation (NCC) as an alternative form of the SAD to evaluate the degree of similarity between two compared images [19,20] because of its advantage that is more robust against illumination variations. The main drawback of this algorithm is that if an object is occluded owing to an occlusion by other objects, image matching becomes very difficult because invalid pixels that belong to the occlusion participate in the template matching process. To overcome these problems, several modified NCC-based approaches have been proposed. A scheme proposed by Ching [21] incorporates occlusion detection and registration by computing the correlation of two images based on all data, then selectively removing regions that are poorly correlated between the two images. Kaneko et al. [22] devised a selective correlation coefficient (SCC) as a variant of Ching’s scheme, where it uses a binary mask derived from an increment sign (IS) between two images to detect an occlusion region and then the binary mask is coupled with the NCC. However, if the object is under high noise environment, the SCC does not work any longer because the high noise components

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prevent from finding a reliable mask whose construction is based on the similarity of sign increment in the adjacent pixels in both images. The purpose of this paper is to present a robust intensitybased image matching algorithm using Occlusion-Free Correlation (OFC) coefficient, which can efficiently handle partially occluded images under low PSNR environment. Our algorithm’s main feature compared to the other methods is to have a reliability assessment step of occlusion detection and thus be able to check if the occlusion detection is appropriately made. The remainder of the paper is organized as follows. Section 2 presents the proposed template matching algorithm including a localization to extract regions of interest (ROI) from the input image and an occlusion detection from an absolute difference image (ADI), developed in this work. In Section 3, the experimental results are compared to those of the traditional intensity-based matching algorithms such as NCC and SCC [22]. Finally, conclusions are presented. 2. Proposed template matching algorithm

Fig. 1. Sliding window on the absolute difference image ADI(t , f uo v o ).

The proposed template matching algorithm performs the following tasks: (i) candidate detection which locates regions of interest (ROIs) in a given image, (ii) occlusion detection which generates a normalized occlusion-detection image, making occlusion regions distinct from non-occluded ones, and (iii) identification which removes the occlusion regions and then classifies the targets. We assume in this study that PSNR is known a priori, uneven illumination is previously compensated for by using an appropriate algorithm and the template matching is conducted under noise environment such as Gaussian, salt & pepper and speckle noise.

It is hard to detect occluded targets in noisy environments using the NCC. Nevertheless, this might be a useful tool in detecting the candidate regions containing potential targets provided that an appropriate threshold is given. In this work, the candidate detection is achieved by performing the NCC between the scene and templates, and then the regions having higher matching score than a certain threshold level TH C are listed as candidates. Given a scene image f (x, y ) of size m1 × m2 and a template image t (x, y ) of size n1 × n2 , where n1  m1 and n2  m2 , the NCC coefficient between the two images with displacement (u , v ) is defined by [15]:

Λ( f uv , t )  [ f uv (x, y ) − f uv ] · [t (x − u , y − v ) − t ] , n1 · n2 x, y σ f · σt 1

where THid is the threshold value of TH C when there is no occlusion. In (4), the threshold THid is given as:

 

THid = mean Λ t , t 



   − std Λ t , t  ,

(5)

mean[·] and std[·] denote the mean and standard deviation by arguments, respectively. (5) says that the higher the variance of noise is, the lower the THid is because Λ(t , t  ) rapidly decreases as the variance of noise increases. However, if t  (x, y ) is further corrupted by an occlusion, the value THid should be set to be lower than that obtained from (5) because the occlusion will make Λ(t , t  ) get lower, resulting in (4). Also, based on the fact that the relationship between THid and the noise variance (σn2 ) differs for each individual template, in this work the relationship of THid versus σn2 was stored in the form of look-up table every template and thereby we could suppress more false alarms than when a single threshold is used in common. 2.2. Occlusion detection

(2)

where α (·) indicates the scaling factor between the two images, f uv (x, y ) and t (x, y ). Let C denote the candidate set consisting of all possible index pairs (u , v ) such that

Λ( f uv , t )  THC ,

(4)

(1)

where −1  Λ(·)  +1, f uv (x, y ) is f (x, y ) within the area of the template shifted to position (u , v ), f uv and t are the mean values, and σ f and σt are the standard deviations of the image f (x, y ) and the template t (x, y ), respectively. In (1), the denominator is related to the scaling factor by which the images are normalized when the brightness of the image and template varies by lighting and exposure conditions,

α ( f uv , t ) = σ f /σt ,

TH C = THid · (1 − ηC ),

where t  (x, y ) is noise-added image to the template t (x, y ), and

2.1. Candidate detection

=

as possible. To do this, the threshold TH C should be determined under the consideration of occlusion rate (ηC ). Given an occlusion rate ηC , the value TH C is given by:

(3)

where TH C is a threshold for detecting the candidate regions. The threshold TH C should be chosen to ensure that the set C includes most of probable candidates with as few false negatives

Occlusion detection is a pre-process for detecting and finally removing occlusion regions from the candidate regions f uv (x, y | (u , v ) ∈ C ), which includes the following procedure. Consider a candidate region f uo v o , where (u o , v o ) ∈ C . Step 1: First, find the absolute difference image ADI(t , f uo v o ) between t (x, y ) and f uo v o (x, y ):

ADI(t , f uo v o )

    = median t (x, y ) − median f uo v o (x, y ) /α ( f uo v o , t ) ,

(6)

where the brightness of f uo v o (x, y ) is adjusted by the scaling factor α (·). Here, the median filter median[·] is used to reduce impulsive noises before and after the calculation of (6) and thereby makes the occlusion detection more exact and reliable, in which 3-by-3 neighborhood median filter is used to preserve edges. Step 2: Scan on the image ADI(t , f uo v o ) using a sliding window of size  by . For a given displacement (dx , d y ), let (i , j ) and P (i , j ) denote pixels’ indexes and their values within the window, respectively (see Fig. 1). And then find O uo v o (x, y ) for

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0  x  n1 − 1 and 0  y  n2 − 1 called occlusion-detection image whose each pixel is represented by the number of pixels such that P (i , j )  THθ within the sliding window at the given displacement (x = d x , y = d y ). That is, O uo v o (x, y ) is given as:



O uo v o (x, y ) = num P (i , j )  THθ



for (x, y ) = (dx , d y ),

(7)

where num[·] indicates the number of pixels in the sliding window satisfying the operation [·]. The discussion about how to choose the best THθ has been given in Section 3.1. Note that the larger the pixel values of O uo v o (x, y ), the more probable the occlusion is. So, (7) makes occlusion regions distinct from non-occluded ones and allows the occlusion regions to be effectively detected and removed from O uo v o (x, y ). If the window size  is too big, O uo v o (x, y ) will have a low resolution in the sense that occlusion regions are not clearly noticeable. Otherwise it is too small, O uo v o (x, y ) will be sensitive to noise. In practice, the determination of the size  has effect on the quality of O uo v o (x, y ) but is not so strict. In this paper, the size  was chosen ad hoc considering the trade-off between resolution of occlusion and its sensitivity to noise:

 = 0.5 × min( O H , O W ),

(8)

where O H and O W indicate the height and width, in pixels, of the occluding object, respectively. Step 3: Finally, find the normalized occlusion-detection image, denoted by E uo v o (x, y ):





E uo v o (x, y ) = O uo v o (x, y )/ max O uo v o (x, y ) .

(9)

Since pixels of E uo v o (x, y ) are normalized between 0 and 1, it is much easier to set a threshold value for detecting occlusion regions than in the unnormalized occlusion-detection image. 2.3. Object identification The objective of this stage is to obtain the image with occlusion removed and reduce false positives through a reliability assessment for the occlusion detection result. It includes the following procedures: (i) First, find the mask image M uo v o (x, y ) which has a value of 0 for all possible index pairs (x, y ) satisfying E uo v o (x, y ) > THOD . That is,



M uo v o (x, y ) =

0 if E uo v o (x, y ) > THOD , 1 otherwise,

(10)

where THOD is a threshold for detecting occlusion regions. Provided that the threshold THOD is optimal, M uo v o (x, y ) will have a value of 0 only for occlusion regions because the values of E uo v o (x, y ) in the occluded regions are larger than those in nonoccluded regions. Here, let’s define the occlusion rate ηuo v o by M uo v o (x, y ) as:



ηu o v o = 1 −

n2 n1 y =1

x=1 median[ M u o v o (x,

n1 · n2

y )]

 .

(11)

In (11), the median filter median[·] is used to prevent spots like salt noise from being treated as occlusion region during the calculation of ηuo v o . (ii) Next, get the occlusion rejected image F uo v o (x, y ) and its corresponding template image T uo v o (x, y ) through the multiplication by the mask M uo v o (x, y ):

F uo v o (x, y ) = f uo v o (x, y ) × M uo v o (x, y ),

(12)

T uo v o (x, y ) = t (x, y ) × M uo v o (x, y ).

(13)

(iii) Next, compute the NCC coefficients λuo v o and

λuo v o = Λ( f uo v o , t ) and μuo v o = Λ( F uo v o , T uo v o ).

μu o v o : (14)

The above two coefficients, λuo v o and μuo v o , are different in that the former is the normalized cross correlation coefficient between the occluded image f uo v o (x, y ) and the template t (x, y ) while the latter is the coefficient between the images free of occlusion, i.e., F uo v o (x, y ) and T uo v o (x, y ). It is important to note here that if occlusion is effectively removed through (12) and (13), then μuo v o will always be somewhat larger than λuo v o and thus the coefficient μuo v o will provide a better identifier in identifying objects that are occluded. (iv) Repeat the above steps (i)–(iii) with THOD = THOD + ε till ηuo v o reaches a minimum allowable occlusion rate of image. THOD in each iteration cycle is increased by ε , any arbitrarily small but positive number, resulting in a smaller ηuo v o . It is finally concluded that the optimal threshold THoOD is determined as a value of THOD that maximizes the difference of μuo v o and λuo v o , i.e.,

THoOD = max [μuo v o − λuo v o ].

(15)

arg THOD

Section 3.2 contains details regarding how the value THOD can be initially set. (v) Finally, with the above optimal threshold THoOD , determine the template t (x, y ) to be in the place corresponding to (u o , v o ) if μuo v o  THoid where μuo v o should be greater than λuo v o . And then the resulting value μuo v o gives the OFC (occlusion-free correlation) coefficient Ω( f uo v o , t ). The above value THoid is a threshold for identifying a target, given as:

THoID = THid (1 − ηuo v o ),

(16) THoOD .

where ηuo v o indicates the occlusion rate at Considering the fact that μuv becomes larger than λuv when the occluded regions are better removed, this step provides an important tool to be able to assess reliability of occlusion detection. For example, when μuo v o < λuo v o meaning that the occlusion detection is not properly carried out, different values of THOD are tried to detect the occlusion more exactly. Also, if there is no THOD satisfying the condition of μuo v o > λuo v o , it indicates that the candidate f uo v o corresponds to a false positive. Therefore, through this reliability assessment of occlusion detection we can not only check if the occlusion detection is truly made well, but also remove many false positives created by TH C in (4). (vi) Repeat the above steps (i) to (v) for ∀(u , v ) ∈ C . 3. Experimental results To test our proposed algorithm, 50 templates and 100 synthetic scenes containing an occluded object were taken and then noises such as Gaussian, salt & pepper and speckle were added to each scene. Those scenes were tested for various levels of noise variance (σ 2 ) of 0.2 to 0.01 in 0.01 increments, which approximately correspond to PSNR between 7 dB and 20 dB. So, totally we obtained 6000 synthetic scenes to be tested. The occlusion rate of the test set ranges around from 20% to 30% under no noise condition, but it results in from 20% to 70% under the above PSNR conditions. Additionally, we verified our approach on 60 noise-added real scenes and then obtained almost the same results with synthetic ones. 3.1. The choice of threshold value THθ Our image matching method requires setting the threshold THθ to obtain the value of O uv (x, y ) in (7). For this purpose, a grayscale normalized histogram based on ADI(t , t  ), which is the absolute difference image between t (x, y ) and t  (x, y ), is considered.

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Fig. 2. Normalized histogram of ADI(t , t  ) and the choice of THθ . (a) Normalized histogram of ADI(t , t  ) under Gaussian noise. (b) THθ which is a minimum of P (i , j ) satisfying the constraint that num[ P (i , j ) < THθ ]/(n1 · n2 )  0.8, where the noise parameter on x-axis indicates noise density (ND) for salt & pepper noise while the variance of noise for the other noises.

Fig. 2(a) shows the pixel brightness data of ADI(t , t  ) plotted as 256-level histograms, where the x-axis represents P (i , j ) with the 0–255 gray-scale levels and the y-axis represents the portion of pixels in the image with that level of brightness. Most values of ADI(t , t  ) are sited in the dark portion of the histogram because of their small values, and their distribution is further concentrated around the dark levels as the variance of noise decreases. In this experiment, the parameter THθ was chosen to ensure that about 80% of pixels in ADI(t , t  ) are not to be voted for O uv (x, y ) during the evaluation of (7). Consequently, the THθ was set to

a minimum of P (i , j ) satisfying the constraint that num[ P (i , j ) < THθ ]/(n1 · n2 )  0.8 for the image ADI(t , t  ) at the displacement (0, 0). Fig. 2(b) shows the relationship of THθ versus σn2 for various noises. 3.2. The choice of threshold value THOD THOD is a threshold for detecting occlusion from the normalized occlusion-detection image E uv (x, y ). In fact, the occlusion region may be quite differently detected according to the choice of THOD .

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Fig. 3. An example of occlusion detection under Gaussian noise. (a) Template t (x, y ). (b) Scene f (x, y ) containing t (x, y ) occluded by a bottle. (c) Scene f (x, y ) corrupted by Gaussian noise of PSNR = 13 dB. (d) Normalized occlusion-detection image E (x, y ). (e) Scene f (x, y ) where occlusion regions are indicated by black spots for explanation. (f) M u v (x, y ) whose occlusion regions are indicated by black spots.

occlusion region (bottle) in which the results of occlusion detection significantly differ according to the choice of THOD . However, besides the problem of finding recursively an optimized THOD , it is important to set its initial value properly. To this end, a gray-scale histogram of the normalized occlusion-detection image is considered. Fig. 5(a) shows the histogram of Fig. 3(d) where most pixels are not occluded and thus are sited in the dark portion of histogram due to their small values. Meanwhile the pixels belonging to occlusion regions are sited in the lighter portion as indicated by shadow area. Fig. 5(b) is the cumulative histogram of Fig. 5(a) showing the sum of all previous frequencies up to the current bin. It allows one to determine what percentage of the data elements in the data set fall above or below a particular value. Considering the fact that the maximum occlusion rate of the test set is 30%, it is appropriate to set one of E (x, y )’s values (for example, 0.18) that are around 70% in the cumulative histogram to be the initial value of THOD . However, in this experiment, E (x, y ) corresponding to 60% was chosen as the initial value of THOD not to miss any occlusion regions while evaluating (10). 3.3. Measures of performance Fig. 4. Results of occlusion detection for various choices of THOD : (a) 0.22; (b) 0.39; (c) 0.59; (d) 0.79.

We recursively chose a THOD as its optimized value that makes μuv be as larger as possible than λuv . This follows from using the fact that μuv is always larger than λuv in case that the occlusion is appropriately well detected. Fig. 3 shows an example of occlusion detection for a given THOD . Fig. 3(c) shows the template image Fig. 3(a) which is hidden by a bottle and corrupted by Gaussian noise of variance of 0.05. Fig. 3(d) shows the resulting normalized occlusion-detection image E (x, y ) whereas Fig. 3(e) shows Fig. 3(b) with occlusion regions indicated by Fig. 3(f). Fig. 4 shows how much important the threshold THOD is in precisely localizing the

The algorithm described in Section 2 was applied to both 6000 synthetic scenes and 60 real images to test our proposed method and then its performance was compared with selective correlation coefficient (SCC) known as the best correlation-based image matching method reported in the literature [22]. Fig. 6 gives the comparison of occlusion detection between the proposed OFC and the SCC under no noise condition while Fig. 7 shows results of how robust the OFC is against noises such as Gaussian, salt & pepper and speckle in detecting the occlusion region when compared to the SCC. It is seen from these figures that the SCC works well under high PSNR conditions, but has severe trouble in deriving a reliable mask image from noisy scene since the construction of the mask image is done based on the similarity of sign increment in

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Fig. 5. An example of histogram of E (x, y ) and its cumulative histogram. (a) Histogram of Fig. 3(d). (b) Cumulative histogram of Fig. 5(a).

the adjacent pixels in both scene and template. As a result, the SCC is very sensitive to noise and thus fails to detect the occlusion region correctly under low PSNR. The results of Fig. 7 prognosticate that bad detection of occlusion by the SCC will cause lots of false negatives, whereas our OFC shows much better performance of occlusion detection with the same conditions on noise. Fig. 8 shows a comparison of the correlation value between the three coefficients Ω(·), Λ(·) and SCC when a vase is occluded by a cup under Gaussian noise environment. Notice that the matching score by Ω(·) is about 10% higher than those of Λ(·) and 5% higher than those

of SCC on average over all noise levels and thus makes the object easier to identify. Similar results were obtained in the experiments with different types of noise including salt & pepper and speckle. In order to quantify the performance of our algorithm, false positive/negative and identification rate were measured. The false positive (FP) rate is the percentage of negative instances misclassified as being positive while the false negative (FN) rate is the proportion of positive instances that were erroneously reported as negative. The identification rate is defined as the ratio of the number of images correctly identified to the total number of

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Fig. 6. Comparison of occlusion detection between Ω(·) and SCC under no noise. (a) Template t (x, y ). (b) Scene f (x, y ). (c) Occlusion regions by Ω(·). (d) Occlusion regions by SCC.

images tested. Three template matching based correlation coefficients (Ω(·), SCC and Λ(·)) are compared in Fig. 9 for various noise levels. In this figure, (a) shows the average identification rate while (b) and (c) show the average FP and FN rate, respectively. As stated early, since the SCC is very sensitive to noise and thus fails to detect the occlusion region correctly under low PSNR. As a result, it generates lots of false negatives as shown in Fig. 9(b). The OFC coefficient Ω(·) identifies much better objects than the SCC and Λ(·) over all PSNR with low FP and FN rate below 10%, where ηC was experimentally set to 0.324 giving the overall best identification with as few false negatives as possible. However, Λ(·) and the SCC have a very large FN rate for a low PSNR aside from that the performance of identification get more worse as noise level increases. We obtained the similar results for Gaussian, salt & pepper and speckle noise, as shown in Fig. 9. On average, the OFC coefficient gave the identification rate of about 90% with FP and FN rate of below 10%. The reason that the performance for salt & pepper noise is somewhat better than that for the other noise types is because the median filter applied to (6) is more effective in removing the salt and pepper noise. These above results clearly show the advantage of using Ω(·). Such better performance is derived from the fact that (i) many false positives are effectively reduced through the reliability assessment of occlusion detection, (ii) THoid is set individually for each template, and (iii) THOD is adaptively chosen based on histogram characteristics of the normalized occlusiondetection image. 4. Conclusion In this work, we have introduced a new intensity-based template matching algorithm using OFC coefficient, which shows a distinctive improvement in identification rate without a noticeable increase of FP rate when objects are partially occluded under such low PSNR conditions that correlation-based matching

Fig. 7. Comparison of occlusion detection between Ω(·) and SCC for three kinds of noise. (a) Occlusion detection for Gaussian noise with σn2 = 0.1. (b) Occlusion detection for salt & pepper noise with ND (Noise Density) = 0.1. (c) Occlusion detection for speckle noise with σn2 = 0.1.

methods don’t work. Our algorithm is robust against occlusion under low PSNR because it uses (i) THoid individually computed for each template so that more false positives are reduced as compared to the case when a single threshold is used in common for all templates, (ii) adaptively adjusted THOD making occlusion regions distinct from non-occluded ones, and (iii) the reliability assessment of occlusion detection allowing for suppressing many false positives. The experimental results show that the proposed method yields 90% correct matching rate and FP & FN rate below 10% on average, signifying its suitability in a wide range of applications for detecting partially occluded object under low PSNR. Compared with NCC and SCC, the computational cost of our algorithm will be much more expensive since it uses a recursive form to find the optimal threshold THoOD maximizing the difference of μuo v o and λuo v o . Moreover its iteration time can be variable image by image depending on the convergence speed to THoOD . Accelerating the convergence speed would be an interesting possible future extension of this work.

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Fig. 8. Comparison of correlation coefficients between Ω(·), SCC and Λ(·) as a function of variance of Gaussian noise.

Fig. 9. Performance of three template matching based correlation coefficients for various

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Jae Chern Yoo received B.S. degree in electronics from Sungkyunkwan University in 1986, and M.S. and Ph.D. degrees in information & communication engineering and electronics from KAIST and POSTECH, Korea, in 1996 and 2001, respectively. His researches of interest are in the area of pattern recognition, neural network, radar signal processing and image processing. Chang Wook Ahn received his Ph.D. degree from the Department of Information and Communications, from the Gwangju Institute of Science and Technology (GIST), Korea, in 2005. He was a visiting scholar at the Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana-Champaign, in 2003. From 2005 to 2007, he was a research staff member at the Communication Research Group, Samsung Advanced Institute of Technology. From 2007 to 2008, he was a research professor at GIST. Currently, he is an associate professor at the Department of Computer Engineering, Sungkyunkwan University. His research areas include evolutionary algorithms, machine learning, and their applications.